The vector-like fermions and scalars contribute to oblique parameters through vacuum polarization diagram for electroweak gauge bosons.
Here we consider \(S\) - and \(T\) -parameters which would constrain our parameter space.
They are given by [1]}
\(& \alpha _{em} S = 4 e^2 \left( \sum _{\rm VLF} \left[ \frac{d}{d q^2} \Pi _{33}^{\rm VLF} - \frac{d}{d q^2} \Pi _{3Q}^{\rm VLF} \right]_{q^2 = 0} + \left[ \frac{d}{d q^2} \Pi _{33}^{h,H} - \frac{d}{d q^2} \Pi _{3Q}^{h,H} \right]_{q^2 = 0} \right), \\& \alpha _{em} T = \frac{e^2}{s_W^2 c_W^2 m_Z^2} \left( \sum _{\rm VLF} \left[ \Pi ^{\rm VLF}_{\pm }(q^2) - \Pi ^{\rm VLF}_{33}(q^2) \right]_{q^2 =0}+ \left[ \Pi ^{h,H}_{\pm }(q^2) - \Pi ^{h,H}_{33}(q^2) \right]_{q^2 =0} \right),\) 
